Thanks for all your quick responses. I'd checked out the Superior Threads site before I posted my desperation plea. That's where I got preferred needle type/size and tension recommendation. I checked for burrs--didn't have any. I put the spool in a mug and now it's working fine.
Yay! Guess I'll have to get a free-standing spool holder.
I pieced this using rayon thread because it was the best color I could find for the backing. I used the rayon in both top thread and bobbin while piecing. It's just a small wallhanging 18 X 24, so it won't be getting any hard use.